There are 132
chairs in a room.

99 of the chairs are red.

What percentage of the chairs are red?

Using the power reducing formulas the expression [tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex].

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

[tex]cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2[/tex]

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

[tex]cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)[/tex]

Now we have:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

Thus,

[tex]cos^4(x) = (1 + cos(2x))/2)^2[/tex]

Now multiplying by 5:

[tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex]

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We can see here that from the available information it is clear that imports of Benin were:

While the exports are:

A locally produced commodity or service that is sold to another nation is referred to as an export. To put it another way, it's a good or service that is sold or sent to another nation to be utilized or consumed there.

Exports may help a nation's economy expand by bringing in money and creating jobs.

Imports are actually known to be goods and services that are brought into a country/nation.

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The height is 230 feet after 9.125 seconds.

We have the  equation that describes the height of the object as a function of time as:

h(t) = -16t^2 + 145t + 2

We input the values and simplify:

-16t^2 + 145t + 2 = 230

-16t^2 + 145t - 228 = 0

we can use the quadratic formula, to solve this quadratic equation,

t = (-b ± √(b^2 - 4ac)) / 2a

where a = -16, b = 145, and c = -228.

t = (-145 ± √(145^2 - 4(-16)(-228))) / 2(-16)

t = (-145 ± √ (21025)) / (-32)

t = (-145 ± 145) / (-32)

t = 0.625 seconds or t = 9.125 seconds

In conclusion, the height is 230 feet after 9.125 seconds.

#complete question:

An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation

When will the height be 230 feet?

Answer:

  D.  9 clubs

Step-by-step explanation:

Given a stem-and-leaf plot of the number of members in clubs, you want to know the number of clubs with 30 or more members.

The plot shows the club membership to be ...

  {10, 13, 15, 24, 26, 30, 36, 39, 50, 55, 59, 61, 66, 78}

The 9 clubs whose member numbers are in bold have at least 30 members.

The number of clubs with at least 30 members is ...

  D.  9 clubs

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Answer:

n + 8

M - x

z - 12

c + d

2f + 20 or 20 + 2f

(x + y)^2 or (x + y) × (x + y)

2mn or 2 × m × n

2b - 6 or 6 - 2b

u^2 + v^2 or v^2 + u^2

(xy)/2 or xy/2

The surface area of the square pyramid given above would be = 400ft²

To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs

where B = base length= 10ft

s = slant height= 15ft

Surface area = 100+2(10×15)

= 100+300

= 400ft²

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Answer: It is 1.24x smaller.

Step-by-step explanation:

1.2(106)= 127.2

1.47(107)= 157.3

157.3/127.2 = 1.24x smaller

The slope from the table is greater than the slope from the graph hence the table shows a greater rate.

The slope of a graph is the measure of how steep a line is. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically, slope is represented as:

Slope (m) = (change in y)/(change in x)

The slope from the table is;

y2 - y1/x2 - x1

m = 42 - 30/7 - 5

= 6

The slope from the graph is;

8 - 0/1.5 - 0

m = 5.33

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No, Jasmine is not completely correct. The commutative property states that the order of the numbers can be changed without affecting the result of the operation.

In addition, the commutative property is true: a + b = b + a for any two numbers a and b.

For subtraction, the commutative property is not true in general: a - b is not equal to b - a.

However, there are some special cases where the commutative property does hold true for subtraction. For example, if a and b are equal, then a - b = b - a.

So, in general, Jasmine's statement that the commutative property never works for subtraction is not correct. While it is true that the commutative property does not hold true for subtraction in the same way that it does for addition, there are some special cases where it does apply.

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The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.

Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.

In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:

[tex](x+2)^2 = x^2 + (x+1)^2[/tex]

Expanding the squares, we get:

[tex]x^2 + 4x + 4 = x^2 + x^2 + 2x + 1[/tex]

Simplifying and rearranging terms, we get:

[tex]2x^2 - 2x - 3 = 0[/tex]

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a

where a = 2, b = -2, and c = -3.

Plugging in these values, we get:

x = (-(-2) ± [tex]\sqrt{((-2)^2 - 4(2)(-3)))[/tex] / 2(2)

x = (2 ± [tex]\sqrt{(4 + 24))[/tex] / 4

x = (2 ± [tex]\sqrt28}[/tex] / 4

x = (2 ± [tex]2\sqrt{7}[/tex]) / 4

x = 1/2 ± [tex]\sqrt{7}[/tex]/2

The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.

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Answer:  formula 9x - 5y = -160 is not a direct variation.

Step-by-step explanation: The provided expression, 9x - 5y = -160, does not exemplify direct variation.

Direct variation is a correlation existing between two variables, wherein one is a constant scalar multiple of the other. Stated differently, should one variable increase by a defined magnitude, the corresponding variable will also experience a commensurate increase of identical magnitude.

The formula provided indicates the absence of a constant proportionality between the temperature in degrees Celsius (x) and the temperature in degrees Fahrenheit (y). It is noteworthy that the correlation amidst the variables x and y is non-linear in nature, thereby precluding its representation in the form of a direct proportionality.

Answer: It is not a direct variation.

Step-by-step explanation:

         While a linear equation is a direct variation, the y-intercept of a direct variation relationship must be 0. Here, that is not the case. Let us manipulate this equation into a slope-intercept equation.

Given:

   9x - 5y = -160

Add 5y and 160 to both sides of the equation:

   5y = 9x + 160

Divide both sides of the equation by 5:

   y = [tex]\frac{9}{5}[/tex]x + 32

32 ≠ 0

the guests arrived for dinner at 6:39 P.M.which is solved by according to given question.

How to solve the question?

To solve this problem, we need to first convert the fraction of an hour that Miss Johnson's guests were late into minutes. We know that 1 hour is equal to 60 minutes, so we can find the number of minutes the guests were late by multiplying 2/5 by 60:

2/5 hour * 60 minutes/hour = 24 minutes

So the guests were 24 minutes late. To find out what time they arrived, we need to add 24 minutes to the original arrival time of 6:15 P.M.:

6:15 P.M. + 24 minutes = 6:39 P.M.

Therefore, the guests arrived for dinner at 6:39 P.M.

It's important to note that fractions can often be confusing when dealing with time calculations. In this case, we converted the fraction of an hour to minutes to make the calculation easier. Additionally, it's always a good idea to double-check your work to ensure that your answer makes sense in the context of the problem.

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Answer: The value of "a" is given by a = 25 - 2b, where "b" is a positive number.

Step-by-step explanation:

Given that log(a) = log15(b) = log25(a + 2b), we can use the properties of logarithms to solve for the value of a.

Since log(a) = log15(b), we can equate the bases and eliminate the logarithms:

a = 15^log15(b) .....(1)

Similarly, since log(a) = log25(a + 2b), we can equate the bases and eliminate the logarithms:

a = (a + 2b)^log25(a + 2b) .....(2)

Now, we can equate the right-hand sides of equations (1) and (2) since they are both equal to a:

15^log15(b) = (a + 2b)^log25(a + 2b)

Taking the logarithm of both sides with base 15, we get:

log15[15^log15(b)] = log15[(a + 2b)^log25(a + 2b)]

Using the property that loga(a^x) = x, we can simplify the left-hand side:

log15(b) = log15[(a + 2b)^log25(a + 2b)]

Now, we can equate the bases and eliminate the logarithms:

b = (a + 2b)^log25(a + 2b)

Taking the logarithm of both sides with base (a + 2b), we get:

log(a + 2b)(b) = log(a + 2b)[(a + 2b)^log25(a + 2b)]

Using the property that loga(a^x) = x, we can simplify the right-hand side:

log(a + 2b)(b) = log25(a + 2b)

Since log(a + 2b)(b) = log(a + 2b)/logb(a + 2b) by the change of base formula, we can rewrite the equation as:

log(a + 2b)/logb(a + 2b) = log25(a + 2b)

Now, we can equate the numerators and denominators separately:

log(a + 2b) = log25(a + 2b)

1 = log25(a + 2b)/(log(a + 2b))

Since loga(a) = 1, we can rewrite the equation as:

log25(a + 2b) = log(a + 2b)/(log(a + 2b))

Using the property that loga(a^x) = x, we get:

log25(a + 2b) = 1

This implies that 25^1 = a + 2b, since we are using the definition of logarithm which states that loga(b) = c is equivalent to a^c = b.

Therefore, a + 2b = 25.

Given that a and b are positive numbers, we can deduce that a + 2b > 0.

Solving for a, we get:

a = 25 - 2b

Since a and b are both positive, a = 25 - 2b > 0.

So, the value of a is greater than zero and is given by a = 25 - 2b, where b is a positive number.

The surface area of the figure is 344 m².

Area is the region bounded by a plane shape.

To calculate the surface area of the figure, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 2

Hence, the area is 344 m².

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Answer:

a. 110°

Positive coterminal angles: 110° + 360° = 470°, 110° + 2(360°) = 830°

Negative coterminal angles: 110° - 360° = -250°, 110° - 2(360°) = -610°

b. 165°

Positive coterminal angles: 165° + 360° = 525°, 165° + 2(360°) = 885°

Negative coterminal angles: 165° - 360° = -195°, 165° - 2(360°) = -555°

c. -10°

Positive coterminal angles: -10° + 360° = 350°, -10° + 2(360°) = 710°

Negative coterminal angles: -10° - 360° = -370°, -10° - 2(360°) = -730°

Step-by-step explanation:

When an angle is in the standard position, it means that the initial side of the angle is the positive x-axis, and the terminal side of the angle is located in one of the four quadrants of the coordinate plane.

To find coterminal angles, we need to add or subtract multiples of 360 degrees to the given angle while keeping the terminal side in the same position. This is because a full rotation around the origin in the coordinate plane is 360 degrees.

For positive coterminal angles, we add multiples of 360 degrees to the given angle. In the case of 110 degrees, we can add 360 degrees once or twice to get 470 degrees or 830 degrees, respectively.

For negative coterminal angles, we subtract multiples of 360 degrees from the given angle. In the case of -10 degrees, we can subtract 360 degrees once or twice to get -370 degrees or -730 degrees, respectively.

It's important to note that there are infinitely many coterminal angles for any given angle, but we usually restrict our answers to the smallest positive and negative angles that differ from the given angle by a multiple of 360 degrees.

Answer:

C. y = 3/2x + 4

Step-by-step explanation:

C. y = 3/2x + 4

Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.

It is a  a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:

We can calculate like this:

Base case: Show that the inequality holds for n=1.

Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).

Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).

Using the inductive hypothesis, we have:

So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:

By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get

Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.

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Answer:

-19

Step-by-step explanation:

First you need to add all of the positive and negative numbers together, which would look like (12+12+24) + (-67) OR 48 + -67. Now add -67 to 48.

-67 + 48 is -19. Therefore the answer is -19.

IM SO SORRY IF THIS DID NOT MAKE SENSE!

Answer:12+12=24

24-67=-43

-43+24=-19

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

12110 × 100

21625

=1211000

21625

=56

Answer is down below!

Step-by-step explanation:

This is of the form h = a + b cos ct, where: a = 40 m. This is the height of the axle of the Ferris wheel. b = -30 m. The magnitude of this number is the radius of the wheel.

The equation that  matches this problem is 15 + 3p = 117

Let the cost of one pair of pants be represented by the variable p.

Then, the cost of three pairs of pants is 3p.

We are also given that the cost of a t-shirt is $15.

The total cost of Amelia's purchase is $117.

Therefore, the equation that matches this problem is:

15 + 3p = 117

This equation represents the total cost of Amelia's purchase, which includes the cost of one t-shirt and three pairs of pants.

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You rented the car for 10 days.

Let's begin by setting up the equation to solve for the number of days:

Total rental cost = (daily rental cost + CDW fee) x number of days + gasoline cost

We know that the daily rental cost is 37.45, and the CDW fee is 19.40, so we can substitute those values into the equation:

646.50 = (37.45 + 19.40) x number of days + 78

Simplifying the equation:

646.50 = 56.85 x number of days + 78

Subtracting 78 from both sides:

568.50 = 56.85 x number of days

Dividing both sides by 56.85:

number of days = 10

Therefore, You rented the car for 10 days.

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The measure of ∠DOT is equal to 58°

The measure of ∠TOU is equal to 32°.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

Mathematically, a complementary angle can be calculated by using this mathematical equation:

Q + R = 90°

Where:

Q and R are measure of the angles subtended.

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;

(7x + 2) + 4x = 90.

11x + 2 = 90

11x = 90 - 2

x = 88/11

x = 8.

For the measure of ∠DOT, we have;

∠DOT = (7x + 2)

∠DOT = 7(8) + 2

∠DOT = 58°

For the measure of ∠TOU, we have;

∠TOU = 4x

∠TOU = 4(8)

∠DOT = 32°.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The amount of time it would take to drain the swimming pool is equal to 75 minutes..

Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:

[tex]P(t) = I(1 - r)^t[/tex]

Where:

Next, we would determine the amount of time it would take to have 0 gallons in the swimming pool:

20 gallons = 3 minutes

5,000 gallons = x minutes

20x = 1500

x = 1500/20

x = 75 minutes.

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Answer: cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

All numbers are positive because it is first quadrant.  Draw a line out.

sin = opp/hypotenuse.  the opposite line of the angle (y) =3

and hypotenuse=4

use pythagorean theorem to find x

4²=3²+x²

[tex]x=\sqrt{7}[/tex]

now use cos=adjacent/hypotenuse

cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]

The firm expects replacing around 734 batteries out of the 32,200 produced.

using the normal distribution formula z = (x - )

When z denotes the z-score,

x denotes the battery life of interest, is the mean battery life, and is the standard deviation.

For x = 100, use the z-score: z = (100 - 120) / 10 z = -2

Calculate the area under the normal curve to the left of z = -2.

0.0228 is the approximate value.

The number of batteries expected to be replaced by the manufacturer is equal to the proportion of batteries with a battery life of less than 100 hours multiplied by the total number of batteries produced:

Number of batteries to be replaced = 0.0228 x 32,200

734.16 batteries are expected to be replaced.

As a result, the firm anticipates replacing around 734 batteries out of the 32,200 produced.

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The probability that the randomly selected person is taking a sunbath is 7/22.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

So, the probability formula is:

P(E) = Favourable events/Total events

Now, insert values in the formula as follows:

P(E) = Favourable events/Total events

P(E) = 28/88

P(E) = 14/44

P(E) = 7/22

Therefore, the probability that the randomly selected person is taking a sunbath is 7/22.

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